pp 1–37 | Cite as

Parameter estimation and diagnostic tests for INMA(1) processes

  • Boris Aleksandrov
  • Christian H. WeißEmail author
Original Paper


The INMA(1) model, an integer-valued counterpart to the usual moving-average model of order 1, gained recently importance for insurance applications. After a comprehensive discussion of stochastic properties of the INMA(1) model, we develop diagnostic tests regarding the marginal distribution (overdispersion, zero inflation) and the autocorrelation structure. We also derive formulae for correcting the bias of point estimators and for constructing joint confidence regions. These inferential approaches rely on asymptotic properties, the finite-sample performance of which is investigated with simulations. A real-data example illustrates the application of the novel diagnostic tools.


Count time series INMA(1) model Diagnostic tests Overdispersion Autocorrelation structure Confidence regions 

Mathematics Subject Classification

60G10 62F03 62F05 62M10 



The authors thank the Associate Editor and the Reviewer for carefully reading the article and for their comments, which greatly improved the article.

Supplementary material

11749_2019_653_MOESM1_ESM.pdf (246 kb)
Supplementary material 1 (pdf 246 KB)


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsHelmut Schmidt UniversityHamburgGermany

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